New numerical methods applied to solving the one-dimensional eigenvalue problem
Abstract
Two new numerical methods, the log derivative and the renormalized Numerov, are developed and applied to the calculation of bound-state solutions of the one-dimensional Schroedinger equation. They are efficient and stable; no convergence difficulties are encountered with double minimum potentials. A useful interpolation formula for calculating eigenfunctions at nongrid points is also derived. Results of example calculations are presented and discussed.
- Publication:
-
Journal of Chemical Physics
- Pub Date:
- November 1977
- DOI:
- 10.1063/1.435384
- Bibcode:
- 1977JChPh..67.4086J
- Keywords:
-
- Eigenvalues;
- Numerical Integration;
- Schroedinger Equation;
- Algorithms;
- Computer Techniques;
- Convergence;
- Eigenvectors;
- Interpolation;
- Iterative Solution;
- Physics (General)